Methods of structuring data, pre-compiled exception list engines, and network appliances

ABSTRACT

A computer executed method is disclosed for sorting a plurality of internet protocol (IP) addresses. The method includes dividing the range of IP addresses into a plurality of clusters representing a plurality of contiguous sub-ranges, assigning each IP address to the cluster associated with the sub-range that includes that IP address, and assigning the IP addresses in each cluster to one of a plurality of pages. If one of the pages has a size less than a page size limit, the method includes duplicating on that page at least one of the IP addresses assigned to that page. For each page, the IP addresses assigned to that page are ordered by numeric value. A network appliance incorporating aspects of the method is also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/171,176 filed on Apr. 21, 2009. The entire disclosure of the aboveapplication is incorporated herein by reference.

FIELD

The present disclosure relates to network security, methods ofstructuring data for high speed searching, pre-compiled exception listengines incorporating such structured data and network appliancesincluding such engines.

BACKGROUND

This section provides background information related to the presentdisclosure which is not necessarily prior art.

There are various known methods of structuring a set of data elementsand of searching the set of data elements to locate a desired element.The data elements may be left unstructured or may be structuredaccording to some principle, such as numerically, alphabetically, etc.The data set may, for example, be searched linearly by looking at eachitem in the set in order or by using a binary search, which repeatedlydivides the set in half and determines whether the desired element isabove, below or equal to the dividing point of the set.

As the number of elements in a data set increases, many known methods ofstructuring and/or searching the data set become cumbersome. Suchmethods may become slower, require more processor power, and/or memory.

SUMMARY

This section provides a general summary of the disclosure, and is not acomprehensive disclosure of its full scope or all of its features.

According to one aspect of the present disclosure, a computer executedmethod is disclosed for sorting a plurality of Internet protocol (IP)addresses, each of which has a numeric value within a range of numericvalues. The method includes dividing the range into a plurality ofclusters representing a plurality of contiguous sub-ranges. Eachsub-range encompasses substantially the same number of numeric values ofthe range and each sub-range associated with a different cluster. Themethod also includes assigning each IP address to the cluster associatedwith the sub-range that includes the numeric value of that IP address.Each cluster has a cluster size defined by the number of IP addressesassigned to that cluster. The IP addresses in each cluster are assignedto one of a plurality of pages. Each page has a page size limit definingthe maximum number of IP addresses that can be assigned to that page.Each page has a page size defined by the number of IP addresses assignedto that page. If one of the pages has a page size less than its pagesize limit, the method includes duplicating on that page at least one ofthe IP addresses assigned to that page to increase the page size of thatpage. For each page, the IP addresses assigned to that page are orderedby numeric value.

According to another aspect of the present disclosure, a computerexecuted method is disclosed for sorting a plurality of internetprotocol (IP) addresses, each of which has a numeric value within arange of numeric values. The method includes dividing the range into aplurality of clusters representing a plurality of contiguous sub-ranges.Each sub-range encompasses substantially the same number of numericvalues of the range and each sub-range associated with a differentcluster. The method also includes assigning each IP address to thecluster associated with the sub-range that includes the numeric value ofthat IP address. Each cluster has a cluster size defined by the numberof IP addresses assigned to that cluster. The method includes orderingthe clusters by cluster size. The IP addresses in each cluster areassigned to one of a plurality of pages. Each page has a same page sizelimit defining the maximum number of IP addresses that can be assignedto that page. Each page has a page size defined by the number of IPaddresses assigned to that page. If one or more of said pages has a pagesize less than its page size limit, the method includes duplicating onsaid page one or more of the IP addresses assigned to that page toincrease the page size of said page to its page size limit. For eachpage, the IP addresses assigned to that page are ordered by numericvalue.

According to yet another aspect of the present disclosure a networkappliance for connection to a first network is disclosed. The applianceincludes at least one input coupled to the first network for receiving apacket from the first network. The packet includes an internet protocol(IP) address. The appliance also includes at least one processor fordetermining whether to allow the packet from the first network toproceed and at least one memory device storing instructions and data.The data includes a plurality of pages storing a plurality of exceptedIP addresses. The excepted IP addresses each has a numeric value withina range. The range is divided into a plurality of contiguous sub-rangesand each page includes one or more of the excepted IP addresses havingnumeric values within one or more of the sub-ranges associated with thatpage. Each page has a page size defined by the number of IP addressesassigned to that page. The excepted IP addresses are assigned to eachpage ordered by numeric value. The at least one processor is configuredvia the instructions to identify the IP address of the packet from thefirst network, identify a target page that will include the IP addressif the IP address is one of the plurality of excepted IP addresses,search the target page to determine if the IP address is one of theexcepted IP addresses in the target page, and process the packet fromthe first network according to whether the IP address is an excepted IPaddress in the target page.

According to another aspect of the present application, a networkappliance for connection to a first network includes at least one inputcoupled to the first network for receiving a packet from the firstnetwork. The packet includes an internet protocol (IP) address. Theappliance includes at least one processor for determining whether toallow the packet from the first network to enter the second network andat least one memory device. The appliance also includes a first enginestored in the memory device. The first engine includes a plurality ofpages storing a plurality of excepted IP addresses. The excepted IPaddresses each has a numeric value within a range of numeric values andthe range is divided into a plurality of contiguous sub-ranges. Eachpage includes one or more of the excepted IP addresses having numericvalues within one or more of the sub-ranges associated with that page.Each page has a page size defined by the number of excepted IP addressesassigned to that page. The excepted IP addresses are assigned to eachpage ordered by numeric value. The first engine also includes a firstfinite state machine (FSM). The first FSM includes instructionsexecutable by the processor to determine the page associated with thesub-range encompassing the IP address and output an indication of thepage associated with the sub-range encompassing the IP address. Theengine also includes instructions executable by the processor to searchthe page associated with the sub-range encompassing the IP address todetermine if the IP address is an excepted IP address, and output anindication of whether the IP address is an excepted IP address. Theprocessor is also configured via instructions stored in the memorydevice to process the packet from the first network according to theindication from the first engine.

Further areas of applicability will become apparent from the descriptionprovided herein. The description and specific examples in this summaryare intended for purposes of illustration only and are not intended tolimit the scope of the present disclosure.

DRAWINGS

The drawings described herein are for illustrative purposes only ofselected embodiments and not all possible implementations, and are notintended to limit the scope of the present disclosure.

FIG. 1 is a flow chart illustrating a computer executed method forsorting a plurality of IP addresses according to one aspect of thepresent disclosure.

FIG. 2 is a block illustration of dividing a range of IP addresses intoa plurality of clusters each having a sub-range of the range.

FIG. 3 is a flow diagram illustrating one embodiment of assigning aplurality of IP addresses to a plurality of clusters.

FIG. 4 is a flow diagram illustrating one embodiment of assigning IPaddresses from clusters to pages according to a first fit algorithm.

FIG. 5 is a flow diagram illustrating one embodiment of assigning IPaddresses from clusters to pages according to a best fit algorithm.

FIG. 6 is a flow diagram illustrating one embodiment of searching todetermine if an IP address is one of a plurality of IP addressesassigned to pages according to the present disclosure.

FIG. 7 is a graphical representation of an example application of amethod for sorting a plurality of IP addresses.

FIG. 8 is a network appliance for connection between two networks andincorporating aspects of the methods disclosed herein.

DETAILED DESCRIPTION

Example embodiments will now be described more fully with reference tothe accompanying drawings.

Example embodiments are provided so that this disclosure will bethorough, and will fully convey the scope to those who are skilled inthe art. Numerous specific details are set forth such as examples ofspecific components, devices, and methods, to provide a thoroughunderstanding of embodiments of the present disclosure. It will beapparent to those skilled in the art that specific details need not beemployed, that example embodiments may be embodied in many differentforms and that neither should be construed to limit the scope of thedisclosure. In some example embodiments, well-known processes,well-known device structures, and well-known technologies are notdescribed in detail.

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting. As usedherein, the singular forms “a”, “an” and “the” may be intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. The terms “comprises,” “comprising,” “including,” and“having,” are inclusive and therefore specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof. As used herein, the term “and/or” includes any and allcombinations of one or more of the associated listed items. The methodsteps, processes, and operations described herein are not to beconstrued as necessarily requiring their performance in the particularorder discussed or illustrated, unless specifically identified as anorder of performance. It is also to be understood that additional oralternative steps may be employed.

According to one aspect of the present disclosure, a method, generallyindicated by the reference numeral 100 in FIG. 1, is disclosed forsorting a plurality of internet protocol (IP) addresses, each of whichhas a numeric value within a range of numeric values. The methodincludes, at 102, dividing the range into a plurality of clustersrepresenting a plurality of contiguous sub-ranges. Each sub-rangeencompasses substantially the same number of numeric values of the rangeand each sub-range associated with a different cluster. The method alsoincludes, at 104, assigning each IP address to the cluster associatedwith the sub-range that includes the numeric value of that IP address.Each cluster has a cluster size defined by the number of IP addressesassigned to that cluster. At 106, the IP addresses in each cluster areassigned to one of a plurality of pages. Each page has a page size limitdefining the maximum number of IP addresses that can be assigned to thatpage. Each page has a page size defined by the number of IP addressesassigned to that page. At 108, if one of the pages has a page size lessthan its page size limit, the method includes duplicating on that pageat least one of the IP addresses assigned to that page to increase thepage size of that page. For each page, the IP addresses assigned to thatpage are ordered at 110 by numeric value.

IP addresses are numerical identifiers of devices in a network. Each IPaddress typically has a numerical value and is stored as a binarynumber. There are multiple IP addresses versions, such as IPv4 and IPv6.IPv4 addresses are 32 bit numbers, while IPv6 addresses are 128 bitnumbers. IPv4 addresses are often represented in human friendly decimalnotation as four three digit numbers separated by decimal points (e.g.000.000.000.000). Extra leading zeros are sometimes removed from thedecimal notation, but are included above for explanatory purposes. Eachof the numbers is actually represented by eight bits. An eight bitnumber can represent decimal numbers between 0 and 255). Thus, each ofthe four numbers of the IP address may be between 0 and 255. The methoddisclosed herein is not version specific and may be used with anyversion of IP addresses. The size of the range encompassing a set of allIP addresses is determined by the bit size of that version's IPaddresses. For example IPv4 addresses are 32 bits long resulting in arange of 2̂32 possible IP addresses. Similarly, the range of IPv6addresses is 2̂128 possible IP addresses. The range of the IP addressesaccording to the method disclosed herein may be the range of allpossible IP addresses (e.g., 0 to 2̂32−1 for IPv4 addresses) or anyappropriate subset of all possible IP addresses.

Whatever the range, the method includes dividing the range into aplurality of clusters representing a plurality of contiguous sub-ranges,an example of which is shown in FIG. 2, and assigning each IP address tothe cluster associated with the sub-range that includes the numericvalue of that IP address. Each of the clusters has cluster size definedby the number of IP addresses assigned to that cluster. The size of thesub-ranges is the number of IP addresses that could be placed in thecluster. In FIG. 2, for example a plurality of IP addresses 200 having arange between 0 and 31, inclusive is divided into four clusters 202,204, 206 and 208. Each cluster 202, 204, 206, 208 has a sub-range sizeof eight possible IP addresses. The size of a cluster 202, 204, 206 or208 depends on how many IP addresses from the plurality of IP addresses200 are encompassed by the sub-range of that cluster 202, 204, 206 or208. A cluster is simply a set. Numerous possible implementations ofclusters are possible. According to some embodiments the clusters areimplemented by a map, an array, a list, a hash table, etc. According toat least one embodiment, the clusters are managed and/or searched usinga Standard Template Library (STL) list.

The plurality of contiguous sub-ranges may be determined in numerousdifferent ways. As will be explained more fully below, after theclusters have been populated with the IP addresses from the plurality ofIP addresses, the IP addresses will be assigned to pages by cluster.Each page may have a page size limit, also known as a maximum size, thatmay be expressed in terms of a number of IP addresses or a bit size.Although page sizes, cluster sizes, and page size limits will bediscussed herein in terms of number of IP addresses, it should beunderstood that bit sizes may be interchangeably used. For example, apage size limit of one IP address is the same as a page size limit of 32bits for IPv4 addresses or 128 bits for IPv6 addresses). Because of thepage size limit, each cluster may have no more IP addresses assigned toit than the page size limit. One technique for determining the pluralityof sub-ranges is to assign each sub-range the same number of numericvalues, where the number of numeric values is equal to the page sizelimit. With such a division, no cluster could include more IP addressesthan the page size limit. This way of dividing the range will work withany number of IP addresses, with any range of IP addresses, and with anydistribution of IP addresses. However, such a division results in a verylarge number of clusters. Additionally, as the plurality of IP addressesmay be widely spread over the range and may not be linearly distributedover the range. Thus there may be many clusters with no IP addresses inthose clusters sub-ranges.

Accordingly, in some embodiments, the range may be divided into as fewclusters as possible while still avoiding any cluster having a clustersize greater than the page size limit. Various techniques, includingvarious heuristic techniques, are available for determining the numberof clusters and the size of the sub-ranges to minimize the number ofclusters and maximize the size of the sub-ranges of the clusters. Onetechnique to minimize the number of clusters is to begin with onecluster. When the IP addresses are assigned to the cluster, as soon as(or if) the number of IP addresses assigned to the cluster exceeds thepage size limit, the assigning is stopped, the number of clusters isdoubled (to two) and the assigning begins again. The process stops andthe cluster size is again doubled as soon as the number of IP addressesassigned to any cluster exceeds the page size limit. The process isrepeated until the number of IP addresses assigned to each cluster isless than or equal to the page size limit. With a large number of IPaddresses such a technique may require numerous iterations and arelatively long time.

Another technique assumes that the IP addresses are relatively linearlydistributed and divide the number of IP addresses in the plurality ofaddresses by the page size limit. Thus, for example, if the page sizelimit is 2̂10 and the number of IP addresses is 2̂16, the number ofclusters is 2̂6. If the range is all IPv4 addresses, the range is 2̂32.Dividing the range (2̂32) by the number of clusters (2̂6) indicates thateach cluster has a sub-range of 2̂26 IP addresses. According to someembodiments this sub-range is then incremented to the next power of two(i.e., incremented to 2̂27 in this example) and the number of clusters iscorrespondingly decreased by a power of two (i.e. decreased to 2̂5 inthis example).

However an initial number of clusters is determined, the iterativetechnique discussed above may be applied to ensure that no cluster has acluster size larger than the page size limit. A flow diagram of theprocess is illustrated in FIG. 3. In the techniques discussed in thepreceding paragraph a linear distribution is assumed. If this assumptionis correct, the number of clusters determined by dividing the number ofIP addresses by the page size limit will result in no cluster having acluster size larger than the page size limit. If however, the IPaddresses are not linearly distributed or possibly if the number ofclusters is decreased by a power of two as discussed above, some of theclusters may have a cluster size greater than the page limit size.According to some embodiments, therefore, the number of clusters isdoubled (increased by a power of two) and the assigning of IP addressesto clusters is restarted when any cluster's cluster size exceeds thepage size limit. The comparison may be done as the IP addresses arebeing assigned to the clusters or after all IP addresses have beenassigned to clusters. Referring again to FIG. 3, at 300 the processbegins with an initial number of clusters. Each cluster has a sub-rangeof a range of IP addresses. The process continues at 302 by determiningif there are any having IP addresses that have not been assigned to acluster. If not, the process is complete at 304 and all IP addresseshave been assigned to clusters. If, however, there are unassigned IPaddresses, the process continues to 306 and the unassigned IP addressesare assigned to the cluster whose sub-range encompasses the unassignedIP address. At 308, the cluster size of the cluster to which theunassigned IP addresses were assigned is compared to the page sizelimit. If the cluster size is not greater than the page size limit, theprocess returns to 302. If the cluster size of the cluster does exceedthe page size limit, at 310 all previously assigned IP addresses areunassigned, the number of clusters is doubled, the size of thesub-ranges is reduced by one-half, and the process returns to 302. Theprocess of stopping, doubling the number of clusters (and decreasing thesize of the sub-ranges) and restarting the assigning of IP addresses toclusters may be repeated until the cluster sizes are all less than orequal to the page size limit. By using this technique and deliberatelystarting with a number of clusters that would result in cluster sizesgreater than the page size limit, the number of clusters can beminimized.

After the IP addresses have been assigned to the appropriate clusters,the clusters may be ordered. The clusters are ordered by cluster size.The ordering may be in order of increasing or decreasing cluster size.Additionally, or alternatively, a cluster list may be created. Thecluster list contains all clusters and their associated data, includingthe IP addresses assigned to each cluster. The clusters may be orderedby cluster size in the cluster list.

The IP addresses in each cluster are assigned to one of a plurality ofpages. In one embodiment, the pages are an array of contiguous memorybytes. Each page has a page size limit defining the maximum number of IPaddresses that can be assigned to that page and a page size defined bythe number of IP addresses assigned to that page. In other embodiments,pages can be implemented in various other ways, such as using binarytrees.

Generally, the page size limit(s) may be any appropriate size. Accordingto some embodiments, however, it is preferred that the page size limitbe a size that will result in a page with a size small enough to bestored in cache memory of a processor with which the page will be used.Such preferred page sizes increase cache locality. Data stored in aprocessor's cache memory may be accessed, manipulated, etc. much fasterthan data stored remote from the processor. Thus, a page size limitsmall enough that a page may be entirely loaded into cache memory mayincrease the speed at which the pages can be searched. Different pagesmay have different page size limits. In some embodiments, however, thepage size limit of each page is the same.

The IP addresses in the clusters may be assigned to pages according tovarious techniques. Initially, at least one page is created. Althoughthe cluster can be simple assigned one cluster to one page, othertechniques may be preferable. Thus, according to some embodiments, theclusters are assigned to pages according to either a first fit or a bestfit algorithm.

Various implementations of first fit algorithms are appropriate and maybe used as part of methods disclosed herein. One example implementationis illustrated by the flow diagram 400 in FIG. 4. When assignedaccording to a first fit algorithm, for each cluster, the existing pagesare searched sequentially, beginning with the first page, to find thefirst page with enough room to hold the IP addresses in the clusterwithout exceeding the page size limit. At 402 the process of assigningIP addresses from each cluster to pages begins. At 404 the processdetermines whether there are any clusters whose IP addresses have notbeen assigned to pages. If there are no such clusters, at 406, theprocess is complete. If there are clusters whose IP addresses have notbeen assigned to pages, the first cluster with unassigned IP addressesis selected at 408 and the existing pages are examined, beginning withthe first page. The process may also begin with the last cluster or anyother appropriate cluster. In the context of this process, the firstpage may be the first page by order, the page with the most IP addresseson the page, the page with the least IP addresses on the page, the lastpage by order, etc. At 410, it is determined whether the cluster's IPaddresses will fit on the retrieved page. If it will, the cluster isassigned to that page at 412 and the process returns to 404. If thecluster's IP addresses will not fit on the page, the process continuesto 414 to determine if there are more existing pages. If there are nomore pages available to examine, a new page is created and the cluster'sIP addresses are assigned to that page at 416 and the process returns to404. If there are additional pages available, the page number to examineis incremented by one, at 418, and the process returns to 410 todetermine if the cluster's IP address will fit on the page.

Various implementations of best fit algorithms are appropriate and maybe used as part of methods disclosed herein. One example implementation500 is illustrated in FIG. 5. When assigned according to a best fitalgorithm, for each cluster, the existing pages are searched todetermine if there is a page with exactly enough room to hold the IPaddresses in the cluster without exceeding the page size limit. Theprocess begins at 502. At 504, the process determines whether there areany clusters whose IP addresses have not been assigned to pages. Ifthere are no such clusters, at 506, the process is complete. If thereare clusters whose IP addresses have not been assigned to pages, thefirst cluster with unassigned IP addresses is selected at 508 and thenumber of IP addresses (referred to in FIG. 5 as X IP addresses)assigned to that cluster (its cluster size) is identified. At 510, theprocess determines if there is an existing page with X empty slots. Thenumber of empty slots, sometimes also referred to herein as freeentries, is the page size limit minus the page size (both expressed innumber of IP addresses) and indicates how many more IP addresses may beassigned to that page without exceeding the page size limit. If there isa page with X empty slots, the cluster's IP addresses are assigned tothat page at 512 and the process returns to 504. If there is no suchpage, the process determines at 514. If not, at 516 a new page iscreated, the cluster's IP addresses are assigned to the new page and theprocess returns to 504. If there are pages with more than X empty slots,X is increased by one at 518 and the process returns to 510.

The assigning of clusters to pages, whether by best fit, first fit, orany other suitable algorithm, continues until each cluster has beenassigned to a page.

According to one embodiment, assignment of IP addresses of the clustersto pages utilizes a cluster list and a page list. As described above,the cluster list contains all clusters and their associated data items.The cluster list is sorted in descending order by the number of entriesin each cluster (i.e. the cluster size). A page list is created thatwill contain pages containing one or more clusters. The page list issorted by the number of free entries (the page size limit minus the pagesize) available for each page. Particularly if a first fit algorithm isbeing used, the page list may be sorted by number of free entries (orempty slots) in ascending order. For each cluster, the cluster isretrieved and the page list is searched for a page that has enough freeentries to hold all the IP addresses in that cluster. This search may beaccording to a first fit algorithm, a best fit algorithm or any othersuitable algorithm. If a page is found with enough free entries, thecluster's IP addresses are assigned to the page and the page list isupdated to reflect the free entries now remaining on the page. If thepage list was ordered by number of free entries, the page list isreordered after each cluster is assigned. If, however, there are nopages with enough free entries, a new page is allocated and the IPaddresses of the first cluster are assigned to the page. The page listis updated to indicate the new page and the number of free entries onthe new page. The process repeats for subsequent clusters until allclusters have been assigned. According to some embodiments, all clustersthat do not include any IP addresses may be assigned to the same page.This page may be page 0, a null page, or any other suitable page. Thisassignment to a null page may speed up searching the IP addresses. Assoon as it is determined that an IP address being search for is in asub-range associated with a cluster assigned to the null page, thesearch can be stopped because the null page includes no IP addresses andtherefore the searched for IP address is not part of the plurality of IPaddresses that have been assigned to the pages.

According to some embodiments, a load factor is determined after all ofthe clusters have been assigned to pages. The load factor is a ratio ofthe sum of the page size limit of the plurality of pages to the numberof IP addresses in the plurality of IP addresses. The load factor may beconsidered the ratio of resources used to amount of data stored. Itrepresents the compactness or efficiency of the pages populated with theIP addresses. The lower the load factor the more compact the populatedpages are. The more pages used for a given number of IP addresses, thehigher the load factor. Similarly, more efficiently populated pages,i.e. pages having page sizes close to or equal to the page size limitwhen populated with the IP addresses, are more likely to result in fewerpages being needed and the load factor may be reduced. If the methodsdisclosed herein are utilized the load factor may be very low. The loadfactor, according to some embodiments, is compared to a load factorthreshold. The load factor threshold can vary based on various factors,including desired speed of processing, amount of memory available in asystem with which the pages will be used, amount of processing poweravailable in a system with which the pages will be used, etc. Accordingto at least one embodiment the load factor threshold is ten percent.According to at least one other embodiment, the load factor threshold isfive percent. If the load factor exceeds the load factor threshold, thepages are not as compact as desired. According to some embodiments, whenthe load factor exceeds the load factor threshold, the number ofclusters is doubled, thereby also decreasing the size of each of thesub-ranges by one-half. The IP addresses are reassigned to the newclusters and the IP addresses in the new clusters assigned to pagesaccording to the methods disclosed above. Because the sub-range of eachnew cluster is one-half what it was previously, most new clusters willhave a smaller cluster size. In many cases, this will permit theclusters to be fit more efficiently into the pages, reducing theunpopulated space in the pages, and decreasing the load factor. If theload factor remains above the load factor threshold, the number ofclusters may again be doubled and this iterative process may continueuntil the load factor is reduced to, or below, the load factorthreshold. Alternatively, or additionally, this process may be repeatedfor a set maximum number of iterations before being stopped. Suchmaximum number of iterations may be useful to prevent the process frombeing repeated too many times and creating more clusters than isdesired.

After the pages have been populated with IP addresses from the clusters,some of the pages may still have free entries remaining. Accordingly, ifone of the pages has a page size less than its page size limit, themethod includes duplicating on that page at least one of the IPaddresses assigned to that page to increase the page size of that page.In some embodiments, the at least one IP address may be duplicated onthe page until the page size is increased to about the page size limit.This duplication of IP addresses to increase the page size to about thepage size limit may be referred to sometimes as padding the pages. Theat least one IP address may be one IP address, possibly repeatedlyduplicated, or it may be multiple IP addresses. The IP address oraddresses to duplicate may be randomly selected or specificallyselected. For example, only the first IP address in a page may beduplicated on the page, only the middle IP address may be duplicated,the IP addresses may be duplicated in order, a single randomly selectedIP address may be duplicated, multiple IP addresses may be randomlyselected and duplicated, etc. In at least one embodiment, the at leastone IP address is a plurality of randomly selected IP addressesduplicated until the page size is about the page size limit.

The method also includes ordering, for each page, the IP addressesassigned to that page by numeric value. This ordering may make searchingthe page easier. Additionally, the padding of the pages, the IPaddresses of which are then ordered by numeric value, may offer somebenefits when the pages are searched. For example, if a page has a pagesize equal to the page size limit, the number of data elements (i.e. IPaddresses) on the page is known. That number of IP addresses is the pagesize limit. Thus, a table lookup may be used during the searching. Themidpoint of the page is a known spot in the page. If a page has 1024 IPaddresses, the midpoint of a padded page is the 512th IP addressregardless of what the values on the page are and regardless of how manydistinct IP addresses are assigned to the page. Additionally, when allpages are so padded and the page size limit of each page is the same,the midpoint of every page is the same. Thus, the midpoint of everypage, and accordingly every subsequent midpoint of the portion above orbelow the midpoint, is a known point, or element, in the page.Particularly using a binary search, sometimes referred to as a divideand conquer search, being able to identify the IP address that is themidpoint without calculation may increase the speed of the search.

According to some embodiments a page record is generated. The pagerecord includes all of the cluster sub-ranges and the page to which theIP addresses in that sub-range are assigned. This data may be arraignedin a tuple of the first numeric value in the sub-range, the last numericvalue in the sub-range and the number of the page with which thesub-range is associated. The page record, however, is not so limited andmay be implemented using any appropriate method of indicating whichsub-range or sub-ranges are associated with each page.

In some embodiments one or more bloom filters may also be created. Bloomfilters are a short-circuit. The bloom filter may be used to identify IPaddresses that are not in the plurality of IP addresses assigned to thepages without actually searching the pages. A separate bloom filter maybe created for each page or a bloom filter may be created for all of thepages. The bloom filter is a bit map having some number of bits, whereeach bit represents a certain number or combination of numbers. Forexample, the first bit of a bloom filter may represent the number 0while the 256th bit represents the number 255. The bloom filter may bemapped to a portion of the IP addresses associated with a page, such asthe bits representing the first decimal number, the last decimal number,etc., such that each bit in the bloom filter is associated with onenumber of the IP address. Alternatively, or additionally, each bit maybe mapped to some combination of numbers of an IP address. Thecombinations of numbers may be the result of a function. Thus, forexample, a bloom filter may represent the first two numbers of an IPaddress exclusive or'd with the last two numbers, or the first numberand'd with the last two numbers, etc. Each bit may be set to a 1 or a 0.If a bit is set to 1, an IP address associated with the page includesthat bits number. Conversely a bit in the bitmap that is set to 0indicates that no IP address on the page includes that bits number. Byway of example, if the IP address 208.77.188.166 is the only numberincluded on a page, all bits of a bloom filter for the first number ofthe IP addresses on the page would be zeros except the 209th bit(representing the number 208), which would be set to 1. In use, bloomfilters may give false positives (i.e. indicate that a number may be ona page when it is in fact not), but not false negatives (i.e. indicatingthat a number is not on a page when in fact it is). Continuing theexample above, if an IP address to be searched for is 208.70.XXX.XXX,the bloom filter indicates that the IP address may be one of the IPaddresses associated with the page (even though it is not in thisexample). Thus the page would still need to be searched to determinethat the address 208.70.XXX.XXX is not an IP address assigned to thepage. Conversely, if the IP address to be searched is 192.XXX.XXX.XXX,by simply looking at the 193 bit of the bloom filter the bloom filterindicates, correctly, that the IP address is not one of the IP addressesassociated with the page. Because bit 193 is a zero, there are no IPaddresses that begin with 192. Accordingly, the page need not besearched. Additionally, a plurality of bloom filters may be used. Eachof the plurality of bloom filters is based on a different number, groupof numbers, function using the numbers, etc. of the IP addresses. Theplurality of bloom filters may be checked sequentially until all bloomfilters indicate that the IP address searched is not within any of thepages, until on of the bloom filters indicates the IP address may be inthe pages, etc. As can be seen, the use of bloom filters may decreasethe amount of time required to determine whether an IP address ispresent within a plurality of IP addresses processed according to thedisclosed methods. This improved performance is particularly notablewhen a large number of IP addresses to be search for will not and/or arenot part of the plurality of IP addresses on the pages.

After one or more of the methods disclosed herein has been performed,the pages containing the IP addresses are ready to be searched. Anycombination of searching the pages directly, searching the page recordto determine on which page to search and/or using the bloom filter todetermine if searching the pages and/or the page record is evennecessary may be used. According to some embodiments, the bloom filteris searched first to determine if an IP address is not an IP addressassociated with one of the pages. If the bloom filter indicates the IPaddress is not an IP address associated with one of the pages, nofurther searching may not be necessary. If the bloom filter indicatesthe IP address may be an IP address associated with one of the pages,the table record may be searched to determine with which page thesub-range encompassing the IP address is associated. After such page isdetermined, the page itself is searched to determine whether the IPaddress is one of the IP addresses assigned to such page.

FIG. 6 illustrate one example process 600 for searching to determine ifan IP address is one of the plurality of IP addresses. In this example,a page record and a null page are used, but no bloom filter is used. At602, the sub-range that encompasses the IP address is determined. Thepage record is searched at 604 to determine which page contains thesub-range encompassing the IP addresses. At 606, whether the pagereturned by the search in 604 is a null page is determined. If thereturned page is a null page, the search is complete at 608 and the IPaddress is not one of the plurality of IP addresses. If the returnedpage is not a null page, the process continues to 610 and the returnedpage is retrieved. The page is then searched for the IP address at 612.If, at 614, the IP address is not on the page, the process is completeat 608 and the IP address is not one of the plurality of IP addresses.If the IP address is on the page, the search is complete at 616 and theIP address is one of the plurality of IP addresses.

The searching according to embodiments discussed herein may be anyappropriate method of searching for a data item. For example the searchmay be a binary search (sometimes referred to as a binary divide andconquer search), a linear search, an interpolation search, a search asdescribed in co-owned and co-pending U.S. patent application Ser. No.11/591,802, etc.

Additionally, or alternatively, the pages created by the methodsdescribed herein and/or the page record may be combined with appropriateinstructions to create an engine for determining whether an input IPaddress is contained in the plurality of IP addresses processedaccording to the methods described above. The engine includes the pageswith their assigned IP addresses, instructions operable to cause aprocessor to search the pages, and a finite state machine (FSM). Theengine may sometimes be referred to as a pre-compiled exception listengine. The FSM includes the page record and instructions operable tocause a processor to search the page record and output an indication ofwhich, if any, page will contain the input IP address if it is present.When an IP address is input to the engine, the FSM searches the pagerecord to identify on which page the sub-range encompassing the input IPaddress is located and outputs an identifier of that page. Theappropriate page is then searched to determine whether the IP address islocated on the page. The engine then outputs a yes or no answer, forexample a 1 or a 0, indicating that the input IP address is or isn't,respectively, one of the plurality of IP addresses. Some or all of theitems discussed above, such as, for example bloom filters, may also, oralternatively, be included in the engine.

A simplified example of the use of the methods described herein will nowbe described with reference to FIG. 7. For simplicity the someintervening steps are not illustrated and will only be described. Forthis example, the plurality of IP addresses 700 will be represented by aset of thirty numbers within a range which is the set of eight bitintegers (i.e., all numbers are between 0 and 255, inclusive). Eachnumber therefore, will have a size of eight bits. The page size limitfor this example is eight IP addresses (or 64 bits). Thus, each clustercan have no more than eight IP addresses assigned to it. A load factorthreshold of 1.5 will be used for this example.

For sake of example, the range is initially divided into only twoclusters. Each cluster has a sub-range of one half the range. The IPaddresses are assigned to the clusters as discussed above. As isapparent, however, there is no way thirty IP addresses can be assignedto two clusters without at least one cluster including more than eightIP addresses. Therefore, the number of clusters is doubled and the sizeof the sub-ranges decreased by one-half. At this point there are fourclusters. The IP addresses are assigned to them as discussed above. Theresult is a first cluster with a sub-range of (0-63) having twelve IPaddresses (2, 3, 5, 11, 13, 33, 34, 41, 45, 50, 51, 60) assigned to it.A second cluster has a sub-range of (64-127) having six IP addresses(65, 66, 82, 83, 84, 85) assigned to it. A third cluster has a sub-rangeof (128-191) having five IP addresses (150, 151, 170, 175, 180) assignedto it. Finally, a fourth cluster has a sub-range of (192-255) havingseven IP addresses (200, 205, 210, 225, 230, 235, 240) assigned to it.The first cluster still contains more than the page size limit of eightIP addresses and will not fit on a page. Therefore, the number ofclusters is again doubled and the size of the sub-ranges is againdecreased by one-half. The IP addresses are reassigned to the newclusters. The result is eight clusters 702-716. Each cluster 702-716 hasa sub-range size of thirty-two possible IP addresses. The sub-range ofeach cluster 702-716 is indicated by SR in FIG. 7. The values of the IPaddresses assigned to each cluster 702-716 are also indicated within thecluster. Finally, the cluster size (labeled as “Size” in each cluster702-716), for each cluster is indicated. For example, the first cluster702 has the sub-range 0 to 31. The IP addresses assigned to the cluster702 are (2, 3, 5, 11 and 13). Thus, the first cluster has a cluster sizeof five.

Because each cluster 702-716 now has a cluster size less than or equalto the page size limit, the IP addresses in each cluster may be assignedto pages 718-724. The clusters are sorted in descending order accordingcluster size. Accordingly, the first cluster is cluster 704, having acluster size of 7, and the last cluster is cluster 708, having a clustersize of 0. In this example, the clusters are assigned according to afirst fit algorithm. Beginning with the largest cluster, cluster 704, apage with enough room to hold all of the IP addresses of cluster 704 issearched for. There are no pages to begin with and, therefore, no pagewith at room for at least seven IP addresses. Accordingly, a page 718 iscreated and the IP addresses from cluster 704 are assigned to it. Thenext largest cluster 706 has a cluster size of six. As the page sizelimit is eight and there are already seven IP addresses assigned to thefirst, and at this point only, page 718, there is not enough room on anyexisting page for the IP addresses of cluster 706. Thus, a second page720 is created and the IP addresses from cluster 706 are assigned to thepage 720. Similarly, neither the first page 718, nor the second page 720has sufficient free entries to hold the IP addresses of the next largestcluster 702. A third page 722 is, therefore, created and the IPaddresses of the cluster 702 are assigned thereto. Again, none of thepages 718, 720 or 722 have enough free entries to hold the four IPaddresses of cluster 716. A fourth page 724 is created, to which the IPaddresses of the cluster 716 are assigned. The next to be assigned iscluster 712, with a cluster size of three. Neither the first page, northe second page has enough room for the three IP addresses of cluster712. The third page 722 however, only contains five IP addresses of theeight that it can hold. Therefore, the IP addresses of cluster 712 canbe, and are, assigned to the third page 722. When the next cluster 714is assigned, the fourth page 724 is the first page having enough freeentries to hold the IP addresses of cluster 714. At this point the firstpage 718 has one free entry, the second page has two free entries, thethird page has zero free entries and the fourth page has one free entry.Cluster 710 is the next largest cluster with two IP addresses. The firstone of the pages 718-724 that can hold the IP addresses in cluster 710is the second page 720, to which the IP addresses are assigned. The lastcluster 708 has no IP addresses and a cluster size of zero. The cluster708 is, therefore, assigned to a null page (which may be page zero),indicating that it includes no IP addresses. All IP addresses in theclusters 702-716 have now been assigned to pages 718-724.

A load factor may be calculated at this point. As discussed above, theload factor is the ratio of the sum of the page size limits to number ofIP addresses in the plurality of IP addresses (or alternatively, butequivalently, to the sum of the page sizes). In this example, the pagesize limit is eight. The sum of the page size limits therefore isthirty-two. The sum of the page sizes and the number of IP addresses inthe plurality of IP addresses 700 is thirty. Thus, the load factor is32/30 or 1.067. This load factor is acceptable (i.e. it is below theload factor threshold of 1.5). If the load factor were above the loadfactor threshold, the number of clusters would be doubled again asdiscussed above and the entire process discussed above is repeated againuntil the load factor is below the load factor threshold.

The IP addresses assigned to each page 718-724 are next sorted innumerical order. The first page 718 and the fourth page 724 have pagesizes (seven in both cases) lass than the page size limit of eight. Foreach page 718, 724 a random IP address is chosen from the IP addressesassigned to that page 718, 724 and duplicated on that page 718, 724. Forthis example, thirty three was duplicated on first page 718, and twohundred ten was duplicated on the fourth page 724. The result is fourpages 726-732 each having a page size equal to the page size limit ofeight.

Either after the IP addresses have been assigned to the pages 726-732 orwhile the IP addresses are being assigned to pages 718-724, a pagerecord may be created. The page record indicates each of the sub-rangesof the clusters 702-716 (typically by starting value and ending value)and the page to which the IP addresses encompassed by that sub-rangewere assigned. The page record can consist of a tuple for each sub-rangeformatted as (start value, end value, page number). Thus, the pagerecord for this example would be: (0,31,3); (32,63,1); (64,95,2);(96,127,0); (128,159,2); (160,191,3); (192,223,4); (224,255,4). Theplurality of IP addresses 700 may now be searched using the pages726-732 and the page record as discussed above and/or an enginegenerated for searching the plurality of IP addresses.

Although primarily discussed in terms of internet protocol (IP)addresses, the methods disclosed herein is not so limited and may beapplied to other types of data. For example, the methods may be appliedto data such as street addresses, social security numbers, driver'slicense numbers, bank check numbers, etc.

Because of the speed at which very large set of IP addresses may besearched according to the methods presented herein, one use for suchmethods is in connection with network devices (also sometimes referredto as appliances). These devices, including appliances such asfirewalls, routers, servers, etc., may receive packets of data from afirst network and process the packets of data. The processing mayinclude processing internal to the appliance (such as, for example,allowing the packet to cause an application to run on the appliance,cause the appliance to transmit data, files, etc. back to the computeroriginating the packet, etc.) and/or may include passing the packets toa second network. These devices may include rules, policies, etc., forwhether to allow certain packets to be processed or to enter the secondnetwork. For example, a firewall may be located between a network andthe internet. The firewall may wish to block packets originating fromand/or addressed to certain IP addresses. These IP addresses may be theIP addresses of known spammers, hackers, foreign governments, etc.Alternatively, or additionally, these appliances may wish to block allpackets except those originating from certain known IP addresses and/orprocess packets from certain IP addresses differently (such as, forexample, prioritizing transmission of the packets, limiting bandwidth,etc.).

Thus, according to one aspect of the present disclosure, and asillustrated in FIG. 8, a network appliance 800 for connection to a firstnetwork 802 is disclosed. The appliance 800 includes at least one input806 coupled to the first network 802 for receiving a packet from thefirst network 802. The packet includes an internet protocol (IP)address. The appliance 800 also includes at least one processor 808 fordetermining whether to allow the packet from the first network 802 toproceed and at least one memory device 810 storing instructions anddata. The data includes a plurality of pages storing a plurality ofexcepted IP addresses. The excepted IP addresses each has a numericvalue within a range. The range is divided into a plurality ofcontiguous sub-ranges and each page includes one or more of the exceptedIP addresses having numeric values within one or more of the sub-rangesassociated with that page. Each page has a page size defined by thenumber of IP addresses assigned to that page. The excepted IP addressesare assigned to each page ordered by numeric value. The at least oneprocessor 808 is configured via the instructions to identify the IPaddress of the packet from the first network 802, identify a target pagethat will include the IP address if the IP address is one of theplurality of excepted IP addresses, search the target page to determineif the IP address is one of the excepted IP addresses in the targetpage, and process the packet from the first network 802 according towhether the IP address is an excepted IP address in the target page.

The processing the packet according to whether the IP address is anexcepted IP address may include processing internal to the appliance 800and/or may include passing the packets to a second network 804. If theprocessor 808 determines to allow the packet to proceed, processinginternal to the appliance 800 may include allowing the packet to causean application to run on the appliance 800, allowing the packet to causethe appliance 800 to transmit data, files, etc. back to the computeroriginating the packet, etc. Thus, for example, the appliance may be aWeb server, network server, etc. that may determine whether to allow aremote user to access a webpage, run a program stored on the server,view/download files stored on the server, etc. The appliance 800 mayalso include at least one output 812 coupled to a second network 804 fortransmitting the packet from the first network 802 to the second network804 if the processor 808 determines to allow the packet from the firstnetwork 802 to enter the second network 804.

According to another aspect of the present application, a networkappliance 800 for connection to a first network 802 includes at leastone input 806 coupled to the first network 802 for receiving a packetfrom the first network 802. The packet includes an internet protocol(IP) address. The appliance 800 includes at least one processor 808 fordetermining whether to allow the packet from the first network 802 toproceed and at least one memory device 810. The appliance 800 alsoincludes a first engine stored in the memory device 810. The firstengine includes a plurality of pages storing a plurality of excepted IPaddresses. The excepted IP addresses each has a numeric value within arange of numeric values and the range is divided into a plurality ofcontiguous sub-ranges. Each page includes one or more of the excepted IPaddresses having numeric values within one or more of the sub-rangesassociated with that page. Each page has a page size defined by thenumber of excepted IP addresses assigned to that page. The excepted IPaddresses are assigned to each page ordered by numeric value. The firstengine also includes a first finite state machine (FSM). The first FSMincludes instructions executable by the processor 808 to determine thepage associated with the sub-range encompassing the IP address. Theengine includes instructions operable to cause the processor to searchthe page associated with the sub-range encompassing the IP address todetermine if the IP address is an excepted IP address and output anindication of whether the IP address is an excepted IP address. Theprocessor 808 is also configured via instructions stored in the memorydevice 810 to process the packet from the first network 802 according tothe indication from the first engine.

The processing of the packet according to the indication from the firstengine may include processing internal to the appliance 800 and/or mayinclude passing the packets to a second network 804. If the processor808 determines to allow the packet to proceed, processing internal tothe appliance 800 may include allowing the packet to cause anapplication to run on the appliance 800, allowing the packet to causethe appliance 800 to transmit data, files, etc. back to the computeroriginating the packet, etc. Thus, for example, the appliance may be aWeb server, network server, etc. that may determine whether to allow aremote user to access a webpage, run a program stored on the server,view/download files stored on the server, etc. The appliance 800 mayalso include at least one output 812 coupled to the second network 802for transmitting the packet from the first network 802 to the secondnetwork 804 if the processor 808 determines to allow the packet from thefirst network 802 to enter the second network 804 via processing thepacket according to the indication from the first engine.

The processor 808 may include cache memory 814. As discussed above,cache memory resides on the processor 808. Accessing, manipulating,acting upon, etc. data occurs much quicker when the data is stored incache memory 814 than when it is stored in separate memory, such asmemory device 810. For this reason, it may be preferable to have thepage size limit of each page be selected such that the entire page willfit in the cache memory 814.

According to various embodiments, the excepted IP addresses may be IPaddresses to be allowed entry to the second network, denied entry to thesecond network, and/or specially processed. Thus, in some embodiments,if a packet's IP address is an excepted address, the packet is preventedfrom entering the second network. In other embodiments, if a packet's IPaddress is an excepted address, the packet is allowed to enter thesecond network. In still other embodiments, if a packet's IP address isan excepted address, the packet is specially processed, such as beingprioritized, rerouted to a different destination (whether within orwithout the second network), etc. The appliance 800 may operate with twoor more sets of pages and page records and/or more than one engine asdescribed above. For example, one engine may include pages havingexcepted IP addresses that are to be blocked, while a second engineincludes excepted IP addresses to be allowed. There may also be morethan one engine with one type of excepted IP address (e.g., blocked,allowed, special, etc.). Thus, a first engine may include excepted IPaddresses of known hackers, while another engine includes excepted IPaddresses of known spammers. Although only two engines are describedabove, there may be more than two. The engines, when there is more thanone, may be prioritized in any appropriate manner. As one example, if anIP address is found by one engine (A), the appliance may restrictbandwidth available to packets from that IP address. IP addresses foundby another engine (B) may be given high priority and increasedbandwidth. If the IP address of an incoming packet is found by bothengine (A) and engine (B), the appliance may need to apply priorityrules to determine how to handle the packet. For example, engine (B) maybe given highest priority and the packet may be given priority, orengine (A) may be given the higher priority and packets from the IPaddress will be permitted limited bandwidth. Additionally, oralternatively, more complex rules of priority may apply (such as Aprioritized over B except when D is also true, etc.).

In various embodiments some or all of the elements of the methoddiscussed above may be incorporated in or used with the appliance 800.Thus, for example, the data may include a page record. The processor 808may be configured by the instructions to identify the target page bysearching the page record. The processor 808 may be configured by theinstructions to determine that there are no excepted addresses in thesub-range encompassing the IP address by searching the page record. Thedata may also include a null page associated with any sub-rangeencompassing no excepted addresses.

In one example embodiment, the appliance 800 is used by setup by a user(sometimes referred to as an administrator). The user may perform themethod discussed above on a computer that is not the appliance 800. Thepage size limit should be selected such that an entire page will fitwithin the cache memory 814 of the appliance's 800 processor 808. Theresulting pages and page records, or the resulting engines are thenuploaded to the appliance 800 and stored in the at least one memorydevice 810. Alternatively, or additionally, the method may be performedwithin the appliance 800 itself if the appliance 800 has enough memory,processing power, etc. When operating, packets from the first networkhave their IP addresses fed to the engines before being allowed to enterthe second network. As discussed above, the engines will perform thesearching and output an indication of whether the IP address of thepacket is in the pages of the engine (i.e., whether it is an excepted IPaddress). Depending on the result and the configuration of the appliance800, the appliance 800 may allow, block, specially treat, etc. thepacket, it may apply some other action to the packet (such as scanningit, copying it, etc.), or it may input the IP address to another engine.Alternatively, or additionally, the IP address of the packet may besimultaneously input to two or more engines (i.e., parallel processed).

The foregoing description of the embodiments has been provided forpurposes of illustration and description. It is not intended to beexhaustive or to limit the invention. Individual elements or features ofa particular embodiment are generally not limited to that particularembodiment, but, where applicable, are interchangeable and can be usedin a selected embodiment, even if not specifically shown or described.The same may also be varied in many ways. Such variations are not to beregarded as a departure from the invention, and all such modificationsare intended to be included within the scope of the invention.

We claim:
 1. A method of sorting a plurality of interne protocol (IP)addresses, each IP address having a numeric value within a range ofnumeric values, the method comprising: dividing the range into aplurality of clusters representing a plurality of contiguous sub-ranges,each sub-range encompassing substantially the same number of numericvalues of the range and each sub-range associated with a differentcluster; assigning each IP address to the cluster associated with thesub-range that includes the numeric value of said IP address, eachcluster having a cluster size defined by the number of IP addressesassigned to that cluster; assigning the IP addresses in each cluster toone of a plurality of pages, each page having a page size limit definingthe maximum number of IP addresses that can be assigned to that page,and each page having a page size defined by the number of IP addressesassigned to that page; if one of said pages has a page size less thanits page size limit, duplicating on said page at least one of the IPaddresses assigned to that page to increase the page size of said page;and ordering, for each page, the IP addresses assigned to said page bynumeric value.
 2. The method of claim 1 wherein each sub-range isassociated with one of the pages and further comprising generating apage record indicating the page associated with each sub-range.
 3. Themethod of claim 1 wherein duplicating comprises duplicating on said pageone or more of the IP addresses assigned to that page to increase thepage size to said page's page size limit.
 4. The method of claim 1wherein assigning comprises assigning the IP addresses in each clusterto one of a plurality of pages in descending cluster size order.
 5. Themethod of claim 1 further comprising ordering the IP addresses bynumeric value prior to assigning each IP address to the clusterassociated with the sub-range that includes the numeric value of said IPaddress.
 6. The method of claim 5 wherein ordering the IP addresses bynumeric value comprises ordering the IP addresses by numeric value inascending order.
 7. The method of claim 1 further comprising orderingthe clusters by cluster size prior to assigning the IP addresses in eachcluster to one of the plurality of pages.
 8. The method of claim 7wherein ordering the clusters comprises ordering the clusters by clustersize in descending order.
 9. The method of claim 1 wherein each page hassubstantially the same page size limit.
 10. The method of claim 9further comprising if a cluster has a cluster size greater than the pagesize limit, decreasing the number of numeric values encompassed by eachsub-range.
 11. The method of claim 10 wherein decreasing the number ofnumeric values encompassed by each sub-range comprises decreasing thenumber of numeric values by one half.
 12. The method of claim 1 whereinthe IP addresses in each cluster are assigned to one of a plurality ofpages according to one of a first fit and a best fit algorithm withoutcausing the page size of said page to exceed the page size limit. 13.The method of claim 1 further comprising determining a load factor afterassigning the IP addresses in each cluster to one of the plurality ofpages, the load factor being a ratio of the sum of the page size limitof the plurality of pages to the number of IP addresses in the pluralityof IP addresses.
 14. The method of claim 13 further comprising if theload factor is greater than a threshold, decreasing the number ofnumeric values encompassed by each sub-range.
 15. The method of claim 1further comprising generating a bloom filter for at least one page, thebloom filter identifying IP addresses that are not assigned to said pagebut are within a sub-range associated with said page.
 16. The method ofclaim 15, further comprising mapping the bloom filter to a portion ofthe IP addresses associated with the at least one page, wherein each bitin the bloom filter is associated with one number of the IP address. 17.The method of claim 1, further comprising generating a single bloomfilter to be used for a plurality of pages comprising a set of pages,the single bloom filter identifying IP addresses that are not assignedto the set of pages.
 18. The method of claim 1, further comprisinggenerating a plurality of bloom filters, each of the plurality of bloomfilters identifying IP addresses that are not assigned to at least onepage.
 19. The method of claim 18, wherein one of the bloom filters ofthe plurality of bloom filters is associated with one number of an IPaddress and another one of the bloom filters of the plurality of bloomfilters is associated with a different number of the IP address.
 20. Themethod of claim 18, wherein one of the bloom filters of the plurality ofbloom filters is associated with one group of numbers of an IP addressand another one of the bloom filters of the plurality of bloom filtersis associated with a different group of numbers of an IP address.